For a fully discrete whole life insurance of 100,000 on (45), you are given:

(i) The gross premium policy value at duration 5 is 5500 and at duration 6 is 7100

(ii) [math]\quad q_{50}=0.009[/math]

(iii) [math]\quad i=0.05[/math]

(iv) Renewal expenses at the start of each year are 50 plus [math]4 \%[/math] of the gross premium.

(v) Claim expenses are 200.

Calculate the gross premium.

• 2200
• 2250
• 2300
• 2350
• 2400

Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Answer: A

[[math]] \begin{aligned} \left({ }_{5} V+0.96 G-50\right)(1.05) & =q_{50}(100,200)+p_{50}{ }_{6} V \\ (5500+0.96 G-50)(1.05) & =(0.009)(100,200)+(1-0.009)(7100) \\ (1.05)(0.96) G+5722.5 & =7937.9 \\ (1.05)(0.96) G & =2215.4 \\ G & =2197.8 \end{aligned} [[/math]]

Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.